Analysis of potential field data in the wavelet domain

Various Green's functions occurring in Poisson potential field theory can be used to construct non-orthogonal, non-compact, continuous wavelets. Such a construction leads to relations between the horizontal derivatives of geophysical field measurements at all heights, and the wavelet transform of the zero height field. The resulting theory lends itself to a number of applications in the processing of potential field data. Some simple, synthetic examples in two dimensions illustrate one inversion approach based upon the maxima of the wavelet transform (multiscale edges). These examples are presented to illustrate, by way of explicit demonstration, the information content of the multiscale edges. We do not suggest that the methods used in these examples be taken literally as a practical algorithm or inversion technique. Rather, we feel that the real thrust of the method is towards physically based, spatially local filtering of geophysical data images using Green's function wavelets, or compact approximations thereto. To illustrate our first steps in this direction, we present some preliminary results of a 3-D analysis of an aeromagnetic survey.     

Regional magnetic and palaeomagnetic correlation in the Grampian Highlands

Summary . An elongated zone of positive magnetic anomalies extends from Northern Ireland to the Shetland Islands. From the total magnetization of the body causing the anomaly and published palaeomagnetic directions corresponding to a range of different possible ages for the remanent magnetization of this body, associated ranges of susceptibility are calculated. These ranges favour a Siluro–Devonian age as most plausible for the remanent magnetization. Such an age is compatible with the known geology of the area.     

Structure and early evolution of the Arabian Sea and East Somali Basin

The Laxmi Ridge is a large-scale basement high buried beneath the sediments of the Indus Fan. The location of the ocean–continent transition (OCT) on this margin has previously been proposed at either the southern edge of the Laxmi Ridge or beyond it towards the India–Pakistan shelf. The former explains the margin-parallel Laxmi Basin as thinned continental crust, the latter as a failed rift of earlier seafloor spreading. To examine the structure of this margin, a reassessment of marine magnetic data has detailed seafloor-spreading magnetic anomalies prior to anomaly 24 in both the Arabian and East Somali basins. The previously identified anomaly 28 is not interpreted as a seafloor-spreading anomaly but as a magnetized basement feature adjacent to, and merging with, the ridge—the Laxmi Spur. New gravity models across the Laxmi Ridge and adjacent margin using ship and satellite data corroborate the existence of underplated crust beneath the Laxmi Ridge and Basin and the location of the OCT at the southern edge of the Ridge. The results are not compatible with the existence of a pre-anomaly 28 phase of seafloor spreading, although large-scale intrusions may be the origin of some of the basement features in the Laxmi Basin. The models also identify the Laxmi Spur as a low-density feature with a natural remanent magnetization (NRM) compatible with serpentinization. The Laxmi Ridge is mapped to the southeast, where it appears to terminate at a point coinciding with the appearance of E–W magnetic lineations and gravity anomalies at 15.5°N. Thereafter it becomes indistinct. This is interpreted as necessary in the reconstruction to the Mascarene Plateau to avoid continental overlap.     

Curie-temperature depth estimation using a self-similar magnetization model

The Earth's crust is magnetized down to the Curie-temperature depth at about 10 to 50 km. This limited depth extent of the crustal magnetization is discernible in the power spectra of magnetic maps of South Africa and Central Asia. At short wavelengths, the power increases as rapidly towards longer wavelengths as expected for a self-similar magnetized crust with unlimited depth extent. Above wavelengths of about 100 km the power starts increasing less rapidly, indicating the absence of deep-seated sources. To quantify this effect we derive the theoretical power spectrum due to a slab carved out of a self-similar magnetization distribution. This model power spectrum matches the power spectra of South Africa and Central Asia for a self-similarity parameter of β = 4 and Curie temperature depths of 15 to 20 km.     

High-resolution mean sea surface computed with altimeter data of Ers-1 (geodetic mission) and topex-poseidon

The remote-sensing satellite ERS-1, launched in 1991 to study the Earth's environment, was placed on a geodetic (168-day repeat) orbit between 1994 April and 1995 March to map, through altimetric measurements, the gravity field over the whole oceanic domain with a resolution of 8 km at the equator in both along-track and cross-track directions. We have analysed the precise altimeter data of the geodetic mission, and, by also using one year of Topex-Poseidon altimeter data, we have computed a global high-resolution mean sea surface. The various steps involved in pre-processing the ERS-1 data consisted of correcting the data for environmental factors, editing, and reducing, through crossover analyses, the radial orbit error, which directly affects sea-surface height measurements. For this purpose, we adjusted sinusoids at 1 and 2 cycle rev⁻¹ along the ERS-1 profiles in order to minimize crossover differences between ERS-1 and yearly averaged Topex-Poseidon profiles. In effect, the orbit of Topex-Poseidon is very accurately determined (within 2–3 cm for the radial component), so Topex-Poseidon altimeter profiles can serve as a reference to reduce the ERS-1 radial orbit error. The ERS-1 residual orbit error was further reduced through a second crossover analysis between all ascending and descending profiles of the geodetic mission. The along-track ERS-1 and Topex-Poseidon data were then interpolated over the whole oceanic domain on a regular grid of 1/16°× 1/16° size. The mapping of the gridded sea-surface heights reveals the very fine structure of the marine geoid, up until now unknown at a global scale. This new data set will be most useful for marine geophysical and tectonic investigations.